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dbeta pbeta qbeta dbinom pbinom qbinom dcauchy pcauchy qcauchy dchisq pchisq qchisq dexp pexp qexp dF pF qF dgamma pgamma qgamma dgeom pgeom qgeom dhypergeom phypergeom qhypergeom dlnorm plnorm qlnorm dlogis plogis qlogis dnbinom pnbinom qnbinom dnorm pnorm qnorm dpois ppois qpois dt pt qt dunif punif qunif dweibull pweibull qweibull erf erfc cnorm
dbeta(x, s1, s2) As in MathcadThe probability density of the beta distribution at x.
S1 and s2 are its two shape parameters, both above 0. It lies between 0 and 1.
A vector of values gives a vector. See also dbeta, pbeta, qbeta and rbeta.
Plain numbers, without units.
pbeta(x, s1, s2) As in MathcadThe cumulative probability of the beta distribution: the chance of a value at or below x.
S1 and s2 are its two shape parameters, both above 0. It lies between 0 and 1.
qbeta goes back. See also dbeta, pbeta, qbeta and rbeta.
Plain numbers, without units.
qbeta(p, s1, s2) As in MathcadThe inverse of pbeta: the value below which a fraction p of the beta distribution lies.
S1 and s2 are its two shape parameters, both above 0. It lies between 0 and 1.
p is a probability, from 0 to 1. See also dbeta, pbeta, qbeta and rbeta.
dbinom(k, n, p) As in MathcadThe probability of exactly k in the binomial distribution.
It counts The number of successes in n trials, each a success with probability p. n is a whole number, 1 or more. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
A vector of counts gives a vector. See also dbinom, pbinom, qbinom and rbinom.
Plain numbers, without units.
pbinom(k, n, p) As in MathcadThe cumulative probability of the binomial distribution: the chance of a value at or below k.
It counts The number of successes in n trials, each a success with probability p. n is a whole number, 1 or more. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
qbinom goes back. See also dbinom, pbinom, qbinom and rbinom.
Plain numbers, without units.
qbinom(p, n, p) As in MathcadThe inverse of pbinom: the smallest count whose cumulative probability reaches p.
It counts The number of successes in n trials, each a success with probability p. n is a whole number, 1 or more.
p is a probability, from 0 to 1. See also dbinom, pbinom, qbinom and rbinom.
dcauchy(x, l, s) As in MathcadThe probability density of the Cauchy distribution at x.
L is its location (the peak) and s its scale, above 0.
A vector of values gives a vector. See also dcauchy, pcauchy, qcauchy and rcauchy.
Plain numbers, without units.
pcauchy(x, l, s) As in MathcadThe cumulative probability of the Cauchy distribution: the chance of a value at or below x.
L is its location (the peak) and s its scale, above 0.
qcauchy goes back. See also dcauchy, pcauchy, qcauchy and rcauchy.
Plain numbers, without units.
qcauchy(p, l, s) As in MathcadThe inverse of pcauchy: the value below which a fraction p of the Cauchy distribution lies.
L is its location (the peak) and s its scale, above 0.
p is a probability, from 0 to 1. See also dcauchy, pcauchy, qcauchy and rcauchy.
dchisq(x, d) As in MathcadThe probability density of the chi-squared distribution at x.
D is its degrees of freedom, above 0.
A vector of values gives a vector. See also dchisq, pchisq, qchisq and rchisq.
Plain numbers, without units.
pchisq(x, d) As in MathcadThe cumulative probability of the chi-squared distribution: the chance of a value at or below x.
D is its degrees of freedom, above 0.
qchisq goes back. See also dchisq, pchisq, qchisq and rchisq.
Plain numbers, without units.
qchisq(p, d) As in MathcadThe inverse of pchisq: the value below which a fraction p of the chi-squared distribution lies.
D is its degrees of freedom, above 0.
p is a probability, from 0 to 1. See also dchisq, pchisq, qchisq and rchisq.
dexp(x, r) As in MathcadThe probability density of the exponential distribution at x.
R is its rate, above 0; the mean is 1/r.
A vector of values gives a vector. See also dexp, pexp, qexp and rexp.
Plain numbers, without units.
pexp(x, r) As in MathcadThe cumulative probability of the exponential distribution: the chance of a value at or below x.
R is its rate, above 0; the mean is 1/r.
qexp goes back. See also dexp, pexp, qexp and rexp.
Plain numbers, without units.
qexp(p, r) As in MathcadThe inverse of pexp: the value below which a fraction p of the exponential distribution lies.
R is its rate, above 0; the mean is 1/r.
p is a probability, from 0 to 1. See also dexp, pexp, qexp and rexp.
dF(x, d1, d2) As in MathcadThe probability density of the F distribution at x.
D1 and d2 are its degrees of freedom, above 0.
A vector of values gives a vector. See also dF, pF, qF and rF.
Plain numbers, without units.
pF(x, d1, d2) As in MathcadThe cumulative probability of the F distribution: the chance of a value at or below x.
D1 and d2 are its degrees of freedom, above 0.
qF goes back. See also dF, pF, qF and rF.
Plain numbers, without units.
qF(p, d1, d2) As in MathcadThe inverse of pF: the value below which a fraction p of the F distribution lies.
D1 and d2 are its degrees of freedom, above 0.
p is a probability, from 0 to 1. See also dF, pF, qF and rF.
dgamma(x, s) As in MathcadThe probability density of the gamma distribution at x.
S is its shape, above 0; its scale is 1, as in Mathcad. For a scale θ, divide x by θ (and the density by θ).
A vector of values gives a vector. See also dgamma, pgamma, qgamma and rgamma.
Plain numbers, without units.
pgamma(x, s) As in MathcadThe cumulative probability of the gamma distribution: the chance of a value at or below x.
S is its shape, above 0; its scale is 1, as in Mathcad. For a scale θ, divide x by θ (and the density by θ).
qgamma goes back. See also dgamma, pgamma, qgamma and rgamma.
Plain numbers, without units.
qgamma(p, s) As in MathcadThe inverse of pgamma: the value below which a fraction p of the gamma distribution lies.
S is its shape, above 0; its scale is 1, as in Mathcad. For a scale θ, divide x by θ (and the density by θ).
p is a probability, from 0 to 1. See also dgamma, pgamma, qgamma and rgamma.
dgeom(k, p) As in MathcadThe probability of exactly k in the geometric distribution.
It counts The number of failures before the first success, each trial a success with probability p. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
A vector of counts gives a vector. See also dgeom, pgeom, qgeom and rgeom.
Plain numbers, without units.
pgeom(k, p) As in MathcadThe cumulative probability of the geometric distribution: the chance of a value at or below k.
It counts The number of failures before the first success, each trial a success with probability p. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
qgeom goes back. See also dgeom, pgeom, qgeom and rgeom.
Plain numbers, without units.
qgeom(p, p) As in MathcadThe inverse of pgeom: the smallest count whose cumulative probability reaches p.
It counts The number of failures before the first success, each trial a success with probability p.
p is a probability, from 0 to 1. See also dgeom, pgeom, qgeom and rgeom.
dhypergeom(k, a, b, n) As in MathcadThe probability of exactly k in the hypergeometric distribution.
It counts The number of successes in a sample of n, drawn without replacement from a successes and b failures. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
A vector of counts gives a vector. See also dhypergeom, phypergeom, qhypergeom and rhypergeom.
Plain numbers, without units.
phypergeom(k, a, b, n) As in MathcadThe cumulative probability of the hypergeometric distribution: the chance of a value at or below k.
It counts The number of successes in a sample of n, drawn without replacement from a successes and b failures. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
qhypergeom goes back. See also dhypergeom, phypergeom, qhypergeom and rhypergeom.
Plain numbers, without units.
qhypergeom(p, a, b, n) As in MathcadThe inverse of phypergeom: the smallest count whose cumulative probability reaches p.
It counts The number of successes in a sample of n, drawn without replacement from a successes and b failures.
p is a probability, from 0 to 1. See also dhypergeom, phypergeom, qhypergeom and rhypergeom.
dlnorm(x, μ, σ) As in MathcadThe probability density of the lognormal distribution at x.
Μ and σ are the mean and standard deviation of its logarithm; σ is above 0.
A vector of values gives a vector. See also dlnorm, plnorm, qlnorm and rlnorm.
Plain numbers, without units.
plnorm(x, μ, σ) As in MathcadThe cumulative probability of the lognormal distribution: the chance of a value at or below x.
Μ and σ are the mean and standard deviation of its logarithm; σ is above 0.
qlnorm goes back. See also dlnorm, plnorm, qlnorm and rlnorm.
Plain numbers, without units.
qlnorm(p, μ, σ) As in MathcadThe inverse of plnorm: the value below which a fraction p of the lognormal distribution lies.
Μ and σ are the mean and standard deviation of its logarithm; σ is above 0.
p is a probability, from 0 to 1. See also dlnorm, plnorm, qlnorm and rlnorm.
dlogis(x, l, s) As in MathcadThe probability density of the logistic distribution at x.
L is its location and s its scale, above 0.
A vector of values gives a vector. See also dlogis, plogis, qlogis and rlogis.
Plain numbers, without units.
plogis(x, l, s) As in MathcadThe cumulative probability of the logistic distribution: the chance of a value at or below x.
L is its location and s its scale, above 0.
qlogis goes back. See also dlogis, plogis, qlogis and rlogis.
Plain numbers, without units.
qlogis(p, l, s) As in MathcadThe inverse of plogis: the value below which a fraction p of the logistic distribution lies.
L is its location and s its scale, above 0.
p is a probability, from 0 to 1. See also dlogis, plogis, qlogis and rlogis.
dnbinom(k, n, p) As in MathcadThe probability of exactly k in the negative binomial distribution.
It counts The number of failures before the nth success, each trial a success with probability p. n is a whole number, 1 or more. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
A vector of counts gives a vector. See also dnbinom, pnbinom, qnbinom and rnbinom.
Plain numbers, without units.
pnbinom(k, n, p) As in MathcadThe cumulative probability of the negative binomial distribution: the chance of a value at or below k.
It counts The number of failures before the nth success, each trial a success with probability p. n is a whole number, 1 or more. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
qnbinom goes back. See also dnbinom, pnbinom, qnbinom and rnbinom.
Plain numbers, without units.
qnbinom(p, n, p) As in MathcadThe inverse of pnbinom: the smallest count whose cumulative probability reaches p.
It counts The number of failures before the nth success, each trial a success with probability p. n is a whole number, 1 or more.
p is a probability, from 0 to 1. See also dnbinom, pnbinom, qnbinom and rnbinom.
dnorm(x, μ, σ) As in MathcadThe probability density of the normal distribution at x.
Μ is its mean and σ its standard deviation, above 0.
A vector of values gives a vector. See also dnorm, pnorm, qnorm and rnorm.
Plain numbers, without units.
pnorm(x, μ, σ) As in MathcadThe cumulative probability of the normal distribution: the chance of a value at or below x.
Μ is its mean and σ its standard deviation, above 0.
qnorm goes back. See also dnorm, pnorm, qnorm and rnorm.
Plain numbers, without units.
qnorm(p, μ, σ) As in MathcadThe inverse of pnorm: the value below which a fraction p of the normal distribution lies.
Μ is its mean and σ its standard deviation, above 0.
p is a probability, from 0 to 1. See also dnorm, pnorm, qnorm and rnorm.
dpois(k, λ) As in MathcadThe probability of exactly k in the Poisson distribution.
It counts The number of events in an interval where λ, above 0, are expected. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
A vector of counts gives a vector. See also dpois, ppois, qpois and rpois.
Plain numbers, without units.
ppois(k, λ) As in MathcadThe cumulative probability of the Poisson distribution: the chance of a value at or below k.
It counts The number of events in an interval where λ, above 0, are expected. A k that isn't a whole number has probability 0, and the cumulative probability counts up to the whole number below it.
qpois goes back. See also dpois, ppois, qpois and rpois.
Plain numbers, without units.
qpois(p, λ) As in MathcadThe inverse of ppois: the smallest count whose cumulative probability reaches p.
It counts The number of events in an interval where λ, above 0, are expected.
p is a probability, from 0 to 1. See also dpois, ppois, qpois and rpois.
dt(x, d) As in MathcadThe probability density of Student's t distribution at x.
D is its degrees of freedom, above 0.
A vector of values gives a vector. See also dt, pt, qt and rt.
Plain numbers, without units.
pt(x, d) As in MathcadThe cumulative probability of Student's t distribution: the chance of a value at or below x.
D is its degrees of freedom, above 0.
qt goes back. See also dt, pt, qt and rt.
Plain numbers, without units.
qt(p, d) As in MathcadThe inverse of pt: the value below which a fraction p of Student's t distribution lies.
D is its degrees of freedom, above 0.
p is a probability, from 0 to 1. See also dt, pt, qt and rt.
dunif(x, a, b) As in MathcadThe probability density of the uniform distribution at x.
Every value from a to b is equally likely; b is above a.
A vector of values gives a vector. See also dunif, punif, qunif and runif.
Plain numbers, without units.
punif(x, a, b) As in MathcadThe cumulative probability of the uniform distribution: the chance of a value at or below x.
Every value from a to b is equally likely; b is above a.
qunif goes back. See also dunif, punif, qunif and runif.
Plain numbers, without units.
qunif(p, a, b) As in MathcadThe inverse of punif: the value below which a fraction p of the uniform distribution lies.
Every value from a to b is equally likely; b is above a.
p is a probability, from 0 to 1. See also dunif, punif, qunif and runif.
dweibull(x, s) As in MathcadThe probability density of the Weibull distribution at x.
S is its shape, above 0; its scale is 1, as in Mathcad. For a scale λ, divide x by λ (and the density by λ).
A vector of values gives a vector. See also dweibull, pweibull, qweibull and rweibull.
Plain numbers, without units.
pweibull(x, s) As in MathcadThe cumulative probability of the Weibull distribution: the chance of a value at or below x.
S is its shape, above 0; its scale is 1, as in Mathcad. For a scale λ, divide x by λ (and the density by λ).
qweibull goes back. See also dweibull, pweibull, qweibull and rweibull.
Plain numbers, without units.
qweibull(p, s) As in MathcadThe inverse of pweibull: the value below which a fraction p of the Weibull distribution lies.
S is its shape, above 0; its scale is 1, as in Mathcad. For a scale λ, divide x by λ (and the density by λ).
p is a probability, from 0 to 1. See also dweibull, pweibull, qweibull and rweibull.
erf(x) As in MathcadThe error function, (2/√π)·∫₀ˣ e^(−t²) dt.
erf(−x) = −erf(x), and erf approaches 1 as x grows. erfc is 1 − erf(x), without losing digits in the tail. pnorm is ½·(1 + erf((x − μ)/(σ·√2))).
erfc(x) As in MathcadThe complementary error function, 1 − erf(x), accurate far into the tail.
cnorm(x) As in MathcadThe cumulative probability of the standard normal distribution at x, as pnorm(x, 0, 1).
Kept from older Mathcad versions. pnorm takes a mean and standard deviation too.